Problem: $h(n) = 7n-4-2(g(n))$ $f(n) = 4n+7+2(g(n))$ $g(t) = -t+2$ $ h(f(7)) = {?} $
Answer: First, let's solve for the value of the inner function, $f(7)$ . Then we'll know what to plug into the outer function. $f(7) = (4)(7)+7+2(g(7))$ To solve for the value of $f$ , we need to solve for the value of $g(7)$ $g(7) = -7+2$ $g(7) = -5$ That means $f(7) = (4)(7)+7+(2)(-5)$ $f(7) = 25$ Now we know that $f(7) = 25$ . Let's solve for $h(f(7))$ , which is $h(25)$ $h(25) = (7)(25)-4-2(g(25))$ To solve for the value of $h$ , we need to solve for the value of $g(25)$ $g(25) = -25+2$ $g(25) = -23$ That means $h(25) = (7)(25)-4+(-2)(-23)$ $h(25) = 217$